Abstract This paper focuses on evaluating a free piston Stirling engine (FPSE) using describing function method along with a genetic algorithm (GA). In this regard, first, the nonlinear terms of the free piston Stirling engine are investigated by describing function technique and then, the stability of system oscillation is demonstrated using the proposed novel method. Indeed, the mentioned idea is characterized via a graphical representation incorporating genetic algorithm. Afterwards, the free piston Stirling engine parameters including the amplitudes of power and displacer pistons, operating frequency, and phase difference between the pistons motions are estimated via this novel strategy. In the sequel, the generating work and output power of FPSE are calculated taking into account the acquired parameters. Subsequently, the simulation results are verified using the practical data of a prototype engine (i.e. SUTech-SR-1). It is found that the simulation outcomes are in a good agreement with the experimental results, through which the validity of proposed method is affirmed. Indeed, this technique not only assures the stable oscillation (i.e. the sufficient condition) of the free piston Stirling engines but also can predict the engine performance including the generated work and output power as well as the values of design parameters. Furthermore, this technique can easily be applied to design problem of other new converters such as thermos-acoustic engines as well.

中文翻译：

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用描述函数技术和遗传算法研究自由活塞斯特林发动机的极限循环

摘要 本文重点研究了使用描述函数法和遗传算法（GA）评估自由活塞斯特林发动机（FPSE）。在这方面，首先，通过描述函数技术研究了自由活塞斯特林发动机的非线性项，然后使用所提出的新方法证明了系统振荡的稳定性。事实上，上述想法的特点是结合了遗传算法的图形表示。然后，通过这种新颖的策略估计自由活塞斯特林发动机参数，包括功率和置换活塞的振幅、工作频率和活塞运动之间的相位差。接下来，结合获取的参数计算FPSE的发电功和输出功率。随后，使用原型发动机（即SUTech-SR-1）的实际数据验证了模拟结果。仿真结果与实验结果吻合较好，验证了所提方法的有效性。事实上，该技术不仅保证了自由活塞斯特林发动机的稳定振荡（即充分条件），而且可以预测发动机性能，包括产生的功和输出功率以及设计参数的值。此外，该技术也可以很容易地应用于其他新转换器的设计问题，例如热声发动机。通过它来肯定所提出方法的有效性。事实上，该技术不仅保证了自由活塞斯特林发动机的稳定振荡（即充分条件），而且可以预测发动机性能，包括产生的功和输出功率以及设计参数的值。此外，这种技术也可以很容易地应用于其他新转换器的设计问题，例如热声发动机。通过它来肯定所提出方法的有效性。事实上，该技术不仅保证了自由活塞斯特林发动机的稳定振荡（即充分条件），而且可以预测发动机性能，包括产生的功和输出功率以及设计参数的值。此外，这种技术也可以很容易地应用于其他新转换器的设计问题，例如热声发动机。